数列{an}首项为1,有关系2Sn^2=2anSn-an(n≥2且n∈N*) 求证数列{1/Sn}是等差数列求{an}

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数列{an}首项为1,有关系2Sn^2=2anSn-an(n≥2且n∈N*) 求证数列{1/Sn}是等差数列求{an}的通项an

太简单了.
2(S_n)^2=2a_nS_n-a_n
=>
2S_n(S_n-a_n)=-a_n
=>
2S_n*S_{n-1}=-a_n
2S_n*S_{n-1}=-(S_n-S_{n-1})
2=-1/S_{n-1}+1/S_n
所以{1/S_n}是等差数列.
S_1=a_1=1 => 1/S_n=2n-1
=> S_n=1/(2n-1)
=> a_n=1/(2n-1)-1/(2n-3)

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数列{an}首项为1,有关系2Sn^2=2anSn-an(n≥2且n∈N*) 求证数列{1/Sn}是等差数列 求{an}

数列{an}首项为1,有关系2Sn^2=2anSn-an(n≥2且n∈N*) 求证数列{1/Sn}是等差数列求{an}